Equilateral triangle

01 What is always true

∠DAB means the angle at A — the middle letter is always the corner, and the outer two say which sides form it.

• All three sides are the same length.

  AB = BC = CA, each 60 units here.

• All three angles are equal.

  ∠CAB = ∠ABC = ∠BCA (60°)

  Why is every angle exactly 60°?

  1. The three sides are equal, and in any triangle equal sides force the angles opposite them to be equal. So all three angles match — call each one a.

  2. A triangle's angles add to 180°, so a + a + a = 180°, which is 3a = 180°.

  3. Divide both sides by 3 and a = 60°. It cannot be anything else, which is why an equilateral triangle never needs measuring.

• All 3 angles add up to 180°.

  True of every 3-sided shape.

02 Why it works

Equal sides force equal angles, and three equal angles sharing 180° must be 60° each. So every equilateral triangle in every question has 60° corners — there is nothing to work out.

It is also isosceles, by the same argument that makes a square a rhombus: isosceles asks for at least two equal sides, and three is at least two. Papers exploit this, so it is worth knowing.

03 Where it sits

See the whole family on Triangles.